CloseDepartment of Civil Engineering, The Faculty of Engineering and Science, Aalborg University

Editor:

Kiureghian, Armen Der, Madanat, Samer, Pestana, Juan M.

Abstract:

A Finite Element Reliability Method (FERM) is introduced to perform reliability analyses on two-dimensional structures in plane stress, modeled by non-linear plasticity theory. FERM is a coupling between the First Order Reliability Method (FORM) and the Finite Element Method (FEM). FERM can be used to estimate the probability of exceeding a critical event, defined by a so-called limit state function. The limit state function is obtained implicitly by non-linear FEM analysis from a realization of random material properties. As the latter can be modeled as random fields varying continuously over the structure, a discretisation into random elements/variables is introduced. To this purpose, both the Midpoint (MP) and the Spatial Average (SA) approach are considered. The failure probability is obtained iteratively based on a first order Taylor series expansion of the limit state function. Thus, the gradient of the limit state function with respect to the random material variables is needed, or equivalently, the design sensitivities of the output to the FEM analysis with respect to the input. To this end, the Conditional Derivative Method (CDM) is used, which is a specialized Direct Differentiation Method (DDM), here adapted to work with a generally formulated plasticity based constitutive model. The approach is exemplified with a steel plate with a hole in bending subjected to a displacement based limit state function.

Type:

Conference paper

Language:

English

Published in:

Applications of Statistics and Probability in Civil Engineering: Proceedings of the 9th International Conference on Applications of Statistics and Probability in Civil Engineering, 2003, p. 283-290